The teaching of basic elementary number theory facts has transcended the mathematics departments in most colleges, and is nowadays often found in computer science curricula within topics such as cryptography and discrete mathematics. It is less known that these facts can also have interesting applications in fields like image processing. A series of original applications is proposed as an aid in the classroom. These range from producing striking effects in color images, to a reversible color-to-grayscale transformation, to fast image scrambling and unscrambling, and "shared secrets" involving images. All involve basic transforms based on the Euclidean and continued fraction algorithms.